If the bike is in a suitcase and nearing(or over) the max weight; place some parts in your carry-on bag(s).
Saddle, spare tires + tubes, pedals(?), etc.

Have flown over a dozen times with my Bromptons over the years; just used a cardboard box. Even with the
standard Brompton(not superlight/X), never went over the size & weight limits. Because the box is very light;
I can stuff other items with the bike. Tools, clothes, spares(tire, tube), shoes, snacks, lights, etc.

Nagoya Station by 1nterceptor, on Flickr

One time I flew from New York City to Los Angeles. As my usual practice; I just used a factory box that I get
from my dealer for free(Thanks BFold!). Landed at LAX; threw the box and rode to my hotel in Anaheim. Return
flight; I made my own box from 2 smaller boxes that were going to the recycling bin:

Brompton folding bike; ready for check-in by 1nterceptor, on Flickr